## Abstract

The orbits space of an irreducible linear representation of a finite group is a variety whose coordinate ring is the ring of invariant polynomials. Boris Dubrovin proved that the orbits space of the standard reflection representation of an irreducible finite Coxeter group W acquires a natural polynomial Frobenius manifold structure. We apply Dubrovin’s method on various orbits spaces of linear representations of finite groups. We find some of them has non or several natural Frobenius manifold structures. On the other hand, these Frobenius manifold structures include rational and trivial structures which are not known to be related to the invariant theory of finite groups.

Original language | English |
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Article number | 22 |

Journal | Mathematical Physics Analysis and Geometry |

Volume | 25 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 2022 |

Externally published | Yes |

## Keywords

- Flat pencil of metrics
- Frobenius manifold
- Invariant rings
- Orbifolds
- Quotient singularities
- Representations of finite groups

## ASJC Scopus subject areas

- Mathematical Physics
- Geometry and Topology